Base de Helicidad y Paridad

TL;DR

This paper explores the helicity basis of the Lorentz group representations, discusses their relation to parity eigenstates, and proposes a new parity operator that commutes with the Hamiltonian in Fock space.

Contribution

It introduces a novel form of the parity operator that commutes with the Hamiltonian within the helicity basis of Lorentz group representations.

Findings

Helicity eigenstates are not parity eigenstates.

A new parity operator commuting with the Hamiltonian is proposed.

Relations to Gelfand-Tsetlin-Sokolik quantum field theory are discussed.

Abstract

We study the theory of the Lorentz group (1/2,0)+(0,1/2) representation in the helicity basis of the corresponding 4-spinors. As Berestetski, Lifshitz and Pitaevskii mentioned, the helicity eigenstates are not the parity eigenstates. Relations with the Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new form of the parity operator (which commutes with the Hamiltonian) is proposed in the Fock space.